Question

-3x^2 +5x +10 = 3x -x^2 +16 -- what is x?

Answer 1

`x=(1+√(11)i)/(2) ,(1-√(11)i)/(2)`

Explanation:

1) Move all terms to one side.

`3{x}^(2)-5x-10+3x-{x}^(2)+16=0`

2) Simplify
`3{x}^(2)-5x-10+3x-{x}^(2)+163x` to
`2x^2-2x+6.`

`2x^2-2x+6=0`

3) Use the Quadratic Formula.

1) In general, given a
`a{x}^(2)+bx+c=0` there exists two solutions where:

`x=(-b+√(b^2-4ac) )/(2a) ,(-b-√(b^2-4ac) )/(2a)`

2) In this case,
`a=2,b=-2` and
`c=6`.

`x=(2+√((-2)^2-4*2*6) )/(2*2) ,(2-√((-2)^2-4*2*6) )/(2*2)`

3) Simplify.

`x=(2+2√(11) i)/(4) ,(2-2√(11)i)/(4)`

4) Simplify solutions.

`x=(1+√(11)i)/(2) ,(1-√(11)i)/(2)`

Hope this helps,

- ROR